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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2017
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/1707.09673 |
| Etiquetas: |
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- We establish a law of the iterated logarithm (LIL) for the set of real numbers whose $n$-th partial quotient is bigger than $α_n$, where $(α_n)$ is a sequence such that $\sum 1/α_n$ is finite. This set is shown to have Hausdorff dimension $1/2$ in many cases and the measure in LIL is absolutely continuous to the Hausdorff measure. The result is obtained as an application of a strong invariance principle for unbounded observables on the limit set of a sequential iterated function system.